What Math Did You Learn?

[onedomino]

However, many students cannot make those connections until later in school, high school for quite a few.

Yes, I agree. That's why I said "beyond simple arithmetic" and gave the examples of algebra and geometry. I think that math taught as a collection of techniques is more difficult to comprehend when presented without the cultural context of its development.

 

[Annie]

Yes, I agree. That's why I said "beyond simple arithmetic" and gave the examples of algebra and geometry. I think that math taught as a collection of techniques is more difficult to comprehend when presented without the cultural context of its development.

Ok, in secondary ed. I concur, though there will still be those 'few' that just never get to this level-which returns us to the discussion between the American v European models.

I do agree with discussions of how a math process is applicable to real life, from the earliest grades on. Funny thing that, kids can always grab the sharing examples for fractions and money examples for decimals, yet these are the areas where the kids have the most problems in grades 3-5. Go figure.

 

[liberalogic]

I agree that much practice, with multiple problems, is necessary to embed math techniques. But math is far more than a collection of techniques for problem solving. There is a difference between the way math is taught and the way it exists in the real world. Beyond simple arithmetic, math should be taught as a history of human development. Many people learn algebra and geometry without ever realizing who invented it and why. Thus, it seems disconnected from the real world and enthusiasm for learning it is diminished. Why did Newton and Leibniz invent the calculus? What was the social pressure that drove them to do it, and what did it allow them to discover? Who were those guys, what were they looking for, and why? Math should be taught in combination with the cultural context of its development: it is a story of human achievement. The sense of wonder and discovery contained in that story is not often delivered by math teachers. Math is taught as a collection of techniques that are often difficult to learn. But real math is an exciting story and the language of discovery.

I agree and disagree with this. Of course math, or any other subject, is useless if we cannot tie it into the world around us in one way or another. But it is the approach that you mention here that, in a way, underpins the Chicago Math. They are so concerned about making connections to real life (hence the elementary program is entitled "Everyday Mathematics") that they sacrifice the integrity of the math itself.

As for the history lessons, I think they should remain in a history class. Extensive cultural context in a math class is a divdersion from the math itself. Let's have them do the math first, then give them the room to explore its historical origins.

 

[Psychoblues]

Blah, blah blah blah blah. You're good at neg reps.

Yes, I agree. That's why I said "beyond simple arithmetic" and gave the examples of algebra and geometry. I think that math taught as a collection of techniques is more difficult to comprehend when presented without the cultural context of its development.

You ain't much on anything else.

 

[onedomino]

I agree and disagree with this. Of course math, or any other subject, is useless if we cannot tie it into the world around us in one way or another. But it is the approach that you mention here that, in a way, underpins the Chicago Math. They are so concerned about making connections to real life (hence the elementary program is entitled "Everyday Mathematics") that they sacrifice the integrity of the math itself.

As for the history lessons, I think they should remain in a history class. Extensive cultural context in a math class is a divdersion from the math itself. Let's have them do the math first, then give them the room to explore its historical origins.

Math has little meaning to most people without its cultural context and that is one of the reasons it is so difficult to learn. I am not talking about simple arithmetic. What is the significance of an algebraic number? Who invented the concept and why? What was the question that algebraic numbers answered? Why was that important? Did the Cartesian plane land from the sky so we could plot numbers on graph paper? It emerged from a cultural and historical context that gave it meaning. It was an answer, not just a technique. It is much more difficult for someone to learn a mathematical technique that is disconnected from the real world, than it is to learn a technique that is derived from and applies directly to life. Did you ever take Symbolic Logic in school? The reason it is so difficult is that it is presented devoid of context. Math does not need to be that way. The cultural and historical context of math is not a diversion. At the most fundamental level, it is the math.